Critical behavior of a charged Bose gas

A fully self-consistent Hartre-Fock theory, using the Coulomb interaction screened by the polarization insertions calculated in the self-consistent random-phase approximation, is applied to the d-dimensional, dense, charged Bose gas at temperatures close to the transition temperature T_c. The quasiparticle energy spectrum is calculated and shown to behave at T_c like ε(k)=Ak^σ for small k, and σ is calculated as a function of the dimensionality d. The change in transition temperature from that of an ideal gas at the same density, and of the chemical potential are shown to be given by (T_c-T_c0)/T_c0 ≈ Xr_s^(d-2)/3 and μ_c ≈Yr_s^2/3, where r_s is the ratio of the interparticle spacing to the Bohr radius. Approximate expressions are given for the coefficients X and Y. The critical exponents are calculated, and the system is shown to obey exact scaling.